1. Field of the Invention
The present invention concerns a method for determining a spatial quality index of regionalised data.
It can be applied more particularly, but not exclusively, to geophysical data, image data obtained by physical methods, such as medical or sonar methods, the non-destructive control of materials, or even to any type of sampling of natural phenomena, such as mines recognition campaigns, geochemical inventories, pollution sensors, satellite data, oceanographic data, water analysis, etc.
2. Description of the Prior Art
The regionalised data is data marked by coordinates inside a space with N dimensions, that is most currently in a one, two or three dimensional geographical space. This data can be either mono or multivariable, that is that one or several variables are measured or calculated at the data points.
The theory of regionalised variables is known under the name of geostatistics. Geostatistics involves applying probabilities to natural phenomena which develop in space over a period of time, hence the prefix xe2x80x98geoxe2x80x99. This theory is shown in detail in the work entitled xe2x80x9cThe theory of regionalised variablesxe2x80x9d by G. MATHERON (Publisher MASSON).
This theory provides the appropriate language and tools for estimating any quantity, a priori unknown, and able to be marked in a given space on the basis of a forcefully fragmentary sampling of this same quantity.
So as to estimate this unknown quantity, geostatistics makes it possible to suitably select the most appropriate probabilistic model for the situation, the geostatistical estimator being known under the name of xe2x80x9ckrigeagexe2x80x9d.
More than the estimation, the probabilistic model also gives an indicator of the accuracy of the estimate. This indicator, known as estimate variance, is a vital tool as it opens the way for a possible control of uncertainties (translated in variance terms).
Within the context of stationary probabilistic models, which assumes the invariance by translating in space the average of the modelised variable, the covariance tool or variogramme is used to quantify the spatial variability of the data.
For a non-stationary model, generalised covariance is used.
The geostatistical models also make it possible to validly anticipate concerning a future state, for example the exploitation of natural resources, when the data available shall be more numerous and the operator needs to deal with estimating problems.
Irrespective of the context for exploiting natural resources, the question here still concerns whether there is sufficient data available to resolve the operational problem.
Added to the intrinsic quality of each data item is the quality of the spatial integration of this data element inside the whole set of data. This is why it is advantageous to complete the experimental reading by a geostatistical control associated with geographical, time or other types of coordinates.
The usual methods for controlling the quality or coherence of sets of regionalised data are either visual or morphological (studies of shapes) or statistical (without taking into account the spatial coordinates). When they are used, filtering methods (frequency or spatial) generally work on monovariable data and on regular grids. As a result, they are ill-adapted to the breaking up of multivariable data irregularly situated in space into anomalistic and coherent components;
Similarly, the definition of the criteria used to define the anomalies is often arbitrary and ill-adapted to experimental verification.
So as to eliminate these drawbacks, the invention proposes quantifying the spatial quality of a set of regionalised data by virtue of determining a geostatistical index known as a xe2x80x9cSpatial Quality Indexxe2x80x9d (SQI) being used to localise a priori anomalistic data and thus judging the quality of the measurements or of the digital processing which have generated the set of data.
The determination of the SQI resolves both the problem of interpretation of the spatial variations of the mono or multivariable data in general terms of anomalies and coherent component and an estimate of the degree of anomalistic or spatial incoherence present in each data element taken individually. The determination of the SQI does not assume any particular arrangement of the data in space and also fully works on data irregularly distributed in space and also on data regularly situated at the nodes of a grid with N dimensions, for example a three-dimensional acquisition grid for acquiring irregularly distributed geophysical data is defined along two data acquisition transversal/longitudinal axes and a third time vertical axis.
Advantageously, this index is determined by means of the method of the invention which includes the following operational stages:
a first phase for identifying the statistical anomalies of a first order on the basis of a set of raw regionalised data, this identification including a stationing of the data via a preliminary extraction of the spatial drifts of said data and the determination of the associated stationary residue of first order so that the value of the average of the residual data is reasonably constant in space, the anomalies being identified and examined on the first order residue so as to provide a first order anomalistic criterion,
a second phase for identifying a second order statistical anomalies with extraction of the components of first order residue considered as anomalies and the components of first order residue considered as coherent in space,
the establishment of a quantified relation (SQI) between any combination of the estimated values of the anomalistic components of the first and/or second order and any combination of the estimated values of the coherent components of the first and/or second order,
the localisation of space anomalies on the basis of the values of the SQI of each regionalised data element.
Advantageously, said drawing up of a quantified relation constitutes the determination for each regionalised data element taken individually of the ratio of a spatial quality index (SQI).
Of course, said identification stages could be carried out by a geostatistical estimation (krigeage) in a non-stationary model for the first phase and in a stationary model for the second phase.
In the first phase, the non-stationary estimation of the spatial drift makes it possible to obtain first order stationary residue on which it is possible to validly calculate and modelise a variogramme.
The interpretation of this variogramme in terms of coherent and anomalistic components results in the estimation per stationary model of the second order anomalistic component.
More particularly, the stationary and non-stationary geostatistical models could use:
the estimation by factorial krigeage of the anomalistic and coherent components of the residue,
the definition of the krigeage surrounding area adapted to the estimation of each of said anomalistic and coherent components.
Of course, in each of said stages, the analysis could be facilitated by a 3D visual control carried out firstly by an interpolation on a xe2x80x9cgridxe2x80x9d file of any irregularly sampled variable originating from a xe2x80x9cpointxe2x80x9d file, and secondly with by means of a colour code associated with the value of the inserted variable.